Finite Group DatabasebetaFinite Group Databasebeta| order | 14700 |
| automorphism | ? |
| homology | Abelianization (H1) = C3×C4 · Schur multiplier (H2) = C1 |
| direct product | #1043×C49⋊C3 |
| Fitting, derived, Hall | C52×C49 ⋊ C3×C4 |
| Hall | C49×#1043 ⋊ C3 |
| Hall | C52×C49⋊C3 ⋊ C4 |
| Sylow | C49 ⋊ C3×#1043 |
| Sylow | C52 ⋊ C4×C49⋊C3 |
| subgroup | G/H | |
|---|---|---|
| center, hypercenter | C1 | G |
| commutator, Fitting, hypocenter | C52×C49 | C3×C4 |
| Frattini | C7 | ΓL(1,𝔽8)×#1043 |
| socle | C52×C7 | C4×ΓL(1,𝔽8) |
| prime radical | C5⋊D5×C49⋊C3 | C2 |
| cosocle | C49×C5⋊D5 | C2×C3 |
| LCS | G ▷ C52×C49 | |
| UCS | C1 | |
144 conjugacy classes of subgroups.
190 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(14700, 108);